Canonical Runge-Kutta-Nyström (RKN) methods for second order ordinary differential equations

DOI10.1016/0898-1221(91)90209-MzbMath0769.65054OpenAlexW2018561231MaRDI QIDQ1192160

Wenjie Zhu, Meng-Zhao Qin

Publication date: 27 September 1992

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(91)90209-m

zbMATH Keywords

order conditionsrooted treescanonicalRunge-Kutta-Nyström methodHamiltonian formsecond order differential equation system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Optimal three-stage implicit exponentially-fitted RKN methods for solving second-order ODEs, Implicit symmetric and symplectic exponentially fitted modified Runge-Kutta-Nyström methods for solving oscillatory problems, Order conditions of two kinds of canonical difference schemes, Gauss-Runge-Kutta-Nyström methods, A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation, Dissipation-preserving spectral element method for damped seismic wave equations, A class of implicit symmetric symplectic and exponentially fitted Runge-Kutta-Nyström methods for solving oscillatory problems, A Hamiltonian framework for wavefield depth continuation in seismic imaging, A fourth order implicit symmetric and symplectic exponentially fitted Runge-Kutta-Nyström method for solving oscillatory problems

Uses Software

• RODAS

Cites Work

• Order Conditions for Canonical Runge–Kutta Schemes
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